scholarly journals Fourier restriction to polynomial curves I: a geometric inequality

2010 ◽  
Vol 132 (4) ◽  
pp. 1031-1076 ◽  
Author(s):  
Spyridon Dendrinos ◽  
James Wright
Keyword(s):  
Geometric Inequality ◽  
Polynomial Curves ◽  
Fourier Restriction

scholarly journals Fourier restriction, polynomial curves and a geometric inequality

2008 ◽  
Vol 346 (1-2) ◽  
pp. 45-48
Author(s):  
Spyridon Dendrinos ◽  
James Wright
Keyword(s):  
Geometric Inequality ◽  
Polynomial Curves ◽  
Fourier Restriction

scholarly journals (n-2)-tightness and curvature of submanifolds with boundary

1978 ◽  
Vol 1 (4) ◽  
pp. 421-431 ◽  
Author(s):  
Wolfgang Kühnel
Keyword(s):  
Euclidean Space ◽  
Geometric Inequality ◽  
Total Absolute Curvature ◽  
Absolute Curvature

The purpose of this note is to establish a connection between the notion of(n−2)-tightness in the sense of N.H. Kuiper and T.F. Banchoff and the total absolute curvature of compact submanifolds-with-boundary of even dimension in Euclidean space. The argument used is a certain geometric inequality similar to that of S.S. Chern and R.K. Lashof where equality characterizes(n−2)-tightness.

scholarly journals On pencils of polynomial curves

1996 ◽  
Vol 111 (1-3) ◽  
pp. 51-57
Author(s):  
D. Daigle
Keyword(s):  
Polynomial Curves

scholarly journals Time-Harmonic Solutions for Maxwell’s Equations in Anisotropic Media and Bochner–Riesz Estimates with Negative Index for Non-elliptic Surfaces

2021 ◽  
Author(s):  
Rainer Mandel ◽  
Robert Schippa
Keyword(s):  
Gaussian Curvature ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Smooth Surfaces ◽  
Negative Index ◽  
Elliptic Surfaces ◽  
Conical Singularities ◽  
Fourier Restriction ◽  
Time Harmonic ◽  
Homogeneous Media

AbstractWe solve time-harmonic Maxwell’s equations in anisotropic, spatially homogeneous media in intersections of $$L^p$$ L p -spaces. The material laws are time-independent. The analysis requires Fourier restriction–extension estimates for perturbations of Fresnel’s wave surface. This surface can be decomposed into finitely many components of the following three types: smooth surfaces with non-vanishing Gaussian curvature, smooth surfaces with Gaussian curvature vanishing along one-dimensional submanifolds but without flat points, and surfaces with conical singularities. Our estimates are based on new Bochner–Riesz estimates with negative index for non-elliptic surfaces.

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